Code | Title | Credits |
---|---|---|
Introduction to Combinatorics | ||
Introduction to Graph Theory | ||
Introduction to Mathematical Logic | ||
Axiomatic Set Theory | ||
Computability Theory | ||
Computational Complexity | ||
Differential Geometry | ||
Real Analysis I | ||
Real Analysis II | ||
Seminar: Topics in Mathematics |
General examination
The general examination consists of two preliminary examinations. One examination is in two to four subjects selected from algebra, analysis, topology, and applied math, and the other is a specialty examination in a research area approved by the department.
Post-candidacy requirements include the successful completion of an additional 24 credits of graduate coursework, including at least 6 credits of MATH 8999 ; the completion of the dissertation; and the successful defense of the dissertation in a final oral examination.
No more than 15 credits in any combination of MATH 6995 and MATH 8999 may be among the student's final 18 credits of required coursework.
Once a student successfully completes 24 post-candidacy credits, they must register for 1 credit of CCAS 0940 each subsequent fall and spring semester until they have successfully defended their dissertation, thereby completing the degree program.
Degree requirements.
In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.
The detailed regulations of the Ph.D. program are the following:
During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.
The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.
To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members. All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.
About the university, research at cambridge.
The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes.
Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.
Programme | Duration | Department |
---|---|---|
3-4 years | DAMTP | |
3-4 years | DPMMS | |
4 years; with a structured first year | DAMTP and DPMMS | |
(by thesis) | 12 months full-time, or 2 years part-time | DAMTP and DPMMS |
Determining whether your interests and ambitions align with our research and expertise is a vital part of the application and admissions process. When we receive your formal application, we will consider the information you provide on your research interests carefully, alongside other factors such as your academic suitability and potential, how you compare to other applicants in the field, and whether we have a suitable academic supervisor with the capacity to take on new students.
We are committed to widening participation in mathematical research at Cambridge. We welcome and encourage applications from people from groups underrepresented in postgraduate study.
Before making an application to study with us we recommend you:
A list of broad research areas is provided below, together with links to further information. Your interests may span more than one area. On your application form you will be asked to indicate at least one broad area of interest. This is to help us direct your application to the most suitable group of people to review it.
The information linked below will take you to lists of supervisors working in each broad research area, with an indication of their availability. You are encouraged to make informal contact with potential supervisors prior to making an application. Initial contact should be made by email. In your email we recommend you provide a concise explanation of your areas of interest, how your research interests align with the supervisor(s) research, and that you highlight any relevant work you have done in this area. We recommend that you attach an up-to-date CV. The purpose of this contact is to enquire on supervisor capacity and willingness to supervise, and to see if there is a good fit between your interests and theirs.
If you haven’t had a response to an informal enquiry, you are still welcome to apply and list the individual concerned on your application form, although you may also wish to consider other options.
On your application form you will be asked to submit a short research summary, details of your research experience and your reasons for applying to undertake a PhD/MPhil with us. Whilst you are not expected to submit a detailed research proposal at any stage of the process, we do want to know that you have considered the areas of research that you wish to pursue.
Click on a research area to find out more about available supervisors and their research:
DAMTP | DPMMS |
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| |
Please note that a large majority of the successful applicants for PhD studentships with the High Energy Physics, and General Relativity & Cosmology (GR) groups will have taken Part III of the Mathematical Tripos.
Each Department works hard to secure funding for as many offer holders as possible, either from within its own funds, in collaboration with funding partners, or via the University Postgraduate Funding Competition. However, funding is not guaranteed via these routes, and you should investigate funding opportunities early in the process to be sure that you can meet advertised deadlines.
[Funding opportunities across the University and Colleges] |
[Includes Gates Cambridge and Cambridge Trusts] |
The following opportunity is for MPhil applicants only: |
The following opportunities are for doctoral applicants only: |
[HEP, GR and Cosmology] |
: Atmosphere-Ocean Dynamics, Theoretical Geophysics, and certain areas of Fluid and Continuum Mechanics [DAMTP project list] |
[via DPMMS] |
All application deadlines are 23:59pm (midnight) UK time on the stated date. So that your application can be given full consideration please apply by the following deadlines:
11 October 2023 | Gates Cambridge Scholars (US citizens only) |
15 December 2023 | (for doctoral applicants only) |
4 January 2024 | All other applications for admission in October, including Gates for non-US citizens. This is our funding deadline. Applications received by this date will be considered for nomination to the University’s Postgraduate Funding Competition. |
Note for PhD applicants:
We will accept applications for an October start up until the general University deadline in May, but your chances of obtaining funding are significantly reduced. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).
Only in exceptional circumstances will we consider admission to a later start date in the academic year (i.e., January or April). If you intend to apply for a later start date please contact us at [email protected] so we can advise you on the feasibility of your plan.
Note for MPhil applicants:
We will accept applications until the general University deadline in February, but you will not be considered for funding. In addition, space limitations may mean that late applications cannot be considered (i.e., the most appropriate supervisor may already have committed to taking other students).
Most interviews are expected to take place in the second half of January.
The purpose of the interview is to try to ascertain the extent of the applicant's relevant knowledge and experience, and to gauge whether their interests and abilities align with the research of the potential supervisor and/or research group. It will most likely consist of a discussion of your background and motivations for applying to the course, as well as some questions on relevant topics.
Not all applicants will be selected for interview.
If you are selected for interview, you will be contacted by email at the address you provided on your application. The email should confirm:
Prior to interview you may declare a disability, serious health problem or caring responsibility which may require reasonable adjustments for the interview to be made.
Due to interviewer availability and the tight admissions timetable, we can usually only rearrange the time and date of your interview under exceptional circumstances.
Both DAMTP and DPMMS make most of their PhD/MPhil admissions decisions for October entry in January and early February, and you should not expect to receive a decision on your application before mid-February (even if you apply much earlier). We expect to have made decisions on all applications by mid-July. The Department makes every effort to take decisions on applications at the earliest opportunity. In some cases, however, it may take some time for a decision to be made. Applications may need to be viewed by several potential supervisors before a final decision can be reached.
To consider your application formally we must receive a complete application form, together with all supporting documents, by the deadline.
You will be notified of the formal outcome of your application via the Applicant Portal.
Following an interview, you can normally expect to receive notification of the outcome within a week or two.
If you are successful, the University’s Postgraduate Admissions Office will issue a formal offer of admission which will outline all your conditions. As processing times can vary, we may also contact you informally to notify you of our decision.
We do not provide formal feedback to applicants who are unsuccessful at either the application or interview stage.
Take a look at our frequently asked questions for PhD applicants.
© 2024 University of Cambridge
Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.
Learn more about Harvard’s Math community and our statement on diversity and inclusion.
The Harvard Griffin GSAS Office of Equity, Diversity, Inclusion & Belonging offers student affinity groups for graduate students and many other resources.
The Harvard University Office for Gender Equity has dedicated GSAS Title IX resource coordinators who work with and support graduate students.
open. The application deadline is December 15, 2021. -->
The application deadline for fall 2024 admission has passed. Applications for fall 2025 admission will open in September 2024.
For information on admissions and financial support, please visit the Harvard Harvard Kenneth C. Griffin Graduate School of Arts and Sciences.
Harvard Griffin GSAS is committed to ensuring that our application fee does not create a financial obstacle. Applicants can determine eligibility for a fee waiver by completing a series of questions in the Application Fee section of the application. Once these questions have been answered, the application system will provide an immediate response regarding fee waiver eligibility.
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Theoretical mathematics is the study of abstract mathematical structures which form the basic framework for the rest of the mathematical sciences. In large part, theoretical mathematics is inspired by intellectual curiosity.
The Doctor of Philosophy (PhD) in mathematics is the highest degree offered by our program. Graduates will have demonstrated their ability to conduct independent scientific research and contribute new mathematical knowledge and scholarship in their area of specialization.
PhD in Applied Mathematics and Theoretical Physics. Overview. Study. Requirements. Finance. How To Apply. This is a three to four-year research programme culminating in submission and examination of a thesis containing substantial original work.
The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics.
The program of studies for a Math Department PhD student is divided into two main parts: Pre- and Post-Candidacy. Before taking the Candidacy Exam, students need to fulfill numerous requirements which ensure solid preparation in core mathematical areas as well in their chosen specialization.
PhD in Mathematics. The doctoral program in the Department of Mathematics offers the personalized attention of a small department while also providing a wide range of faculty who offer expertise to support dissertation research.
Ph.D. Program. Degree Requirements. In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics.
PhD Program in Applied Mathematics. Students must complete the following requirements in order to earn a PhD in Applied Mathematics. Some specializations have specific course requirements for the doctorate; elective courses are determined in consultation with the program adviser.
The Faculty of Mathematics offers three doctoral (PhD) and one MPhil research programmes. Select a course below to visit the University’s Course Directory where you can read about the structure of the programmes, fees and maintenance costs, entry requirements and key deadlines.
Welcome to the Math PhD program at Harvard University and the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences. Learn more about Harvard’s Math community and our statement on diversity and inclusion.